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arXiv · 1911.03254

Flatness produced by some geometric PDEs

Iulia Hirica·Constantin Udriste·Gabriel Pripoae·Ionel Tevy
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Abstract

This paper has several goals. The first idea is to study the geometric PDEs of connection-flatness, curvature-flatness, Ricci-flatness, scalar curvature-flatness in a modern and rigorous way. Although the idea is not new, our main Theorems about flatness introduce a different point of view in Differential Geometry. The second idea is to introduce and study the Euler-Lagrange prolongations of PDEs-flatness solutions via associated least squares Lagrangian densities and functionals on Riemannian manifolds. All geometric PDEs turned into one of the most intensively developing branches of modern differential geometry.

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Iulia Hirica, Constantin Udriste, Gabriel Pripoae, Ionel Tevy. 2019-11-06. Flatness produced by some geometric PDEs. https://arxiv.org/abs/1911.03254

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